
// Copyright (c) 2010 libmv authors.
//
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// of this software and associated documentation files (the "Software"), to
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// IN THE SOFTWARE.

// Copyright (c) 2012, 2013 Pierre MOULON.

// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "numeric.h"
#include "poly.h"
#include "solver_fundamental_kernel.hpp"


namespace openMVG {
namespace fundamental {
namespace kernel {

using namespace std;
void SevenPointSolver::Solve(const Mat &x1, const Mat &x2, vector<Mat3> *F) {
    assert(2 == x1.rows());
    assert(7 <= x1.cols());
    assert(x1.rows() == x2.rows());
    assert(x1.cols() == x2.cols());

    Vec9 f1, f2;
    if (x1.cols() == 7) {
        // Set up the homogeneous system Af = 0 from the equations x'T*F*x = 0.
        typedef Eigen::Matrix<double, 9, 9> Mat9;
        // In the minimal solution use fixed sized matrix to let Eigen and the
        //  compiler doing the maximum of optimization.
        Mat9 A = Mat::Zero(9, 9);
        EncodeEpipolarEquation(x1, x2, &A);
        // Find the two F matrices in the nullspace of A.
        Nullspace2(&A, &f1, &f2);
    } else {
        // Set up the homogeneous system Af = 0 from the equations x'T*F*x = 0.
        Mat A(x1.cols(), 9);
        EncodeEpipolarEquation(x1, x2, &A);
        // Find the two F matrices in the nullspace of A.
        Nullspace2(&A, &f1, &f2);
    }

    Mat3 F1 = Map<RMat3>(f1.data());
    Mat3 F2 = Map<RMat3>(f2.data());

    // Then, use the condition det(F) = 0 to determine F. In other words, solve
    // det(F1 + a*F2) = 0 for a.
    double a = F1(0, 0), j = F2(0, 0), b = F1(0, 1), k = F2(0, 1), c = F1(0, 2), l = F2(0, 2), d = F1(1, 0),
           m = F2(1, 0), e = F1(1, 1), n = F2(1, 1), f = F1(1, 2), o = F2(1, 2), g = F1(2, 0), p = F2(2, 0),
           h = F1(2, 1), q = F2(2, 1), i = F1(2, 2), r = F2(2, 2);

    // Run fundamental_7point_coeffs.py to get the below coefficients.
    // The coefficients are in ascending powers of alpha, i.e. P[N]*x^N.
    double P[4] = {
        a * e * i + b * f * g + c * d * h - a * f * h - b * d * i - c * e * g,
        a * e * r + a * i * n + b * f * p + b * g * o + c * d * q + c * h * m + d * h * l + e * i * j + f * g * k -
            a * f * q - a * h * o - b * d * r - b * i * m - c * e * p - c * g * n - d * i * k - e * g * l - f * h * j,
        a * n * r + b * o * p + c * m * q + d * l * q + e * j * r + f * k * p + g * k * o + h * l * m + i * j * n -
            a * o * q - b * m * r - c * n * p - d * k * r - e * l * p - f * j * q - g * l * n - h * j * o - i * k * m,
        j * n * r + k * o * p + l * m * q - j * o * q - k * m * r - l * n * p};

    // Solve for the roots of P[3]*x^3 + P[2]*x^2 + P[1]*x + P[0] = 0.
    double roots[3];
    int num_roots = SolveCubicPolynomial(P, roots);

    // Build the fundamental matrix for each solution.
    for (int kk = 0; kk < num_roots; ++kk) {
        F->push_back(F1 + roots[kk] * F2);
    }
}

void EightPointSolver::Solve(const Mat &x1, const Mat &x2, vector<Mat3> *Fs) {
    assert(2 == x1.rows());
    assert(8 <= x1.cols());
    assert(x1.rows() == x2.rows());
    assert(x1.cols() == x2.cols());

    Vec9 f;
    if (x1.cols() == 8) {
        typedef Eigen::Matrix<double, 9, 9> Mat9;
        // In the minimal solution use fixed sized matrix to let Eigen and the
        //  compiler doing the maximum of optimization.
        Mat9 A = Mat::Zero(9, 9);
        EncodeEpipolarEquation(x1, x2, &A);
        Nullspace(&A, &f);
    } else {
        MatX9 A(x1.cols(), 9);
        EncodeEpipolarEquation(x1, x2, &A);
        Nullspace(&A, &f);
    }

    Mat3 F = Map<RMat3>(f.data());

    // Force the fundamental property if the A matrix has full rank.
    // HZ 11.1.1 pag.280
    if (x1.cols() > 8) {
        // Force fundamental matrix to have rank 2
        Eigen::JacobiSVD<Mat3> USV(F, Eigen::ComputeFullU | Eigen::ComputeFullV);
        Vec3 d = USV.singularValues();
        d[2] = 0.0;
        F = USV.matrixU() * d.asDiagonal() * USV.matrixV().transpose();
    }
    Fs->push_back(F);
}

} // namespace kernel
} // namespace fundamental
} // namespace openMVG
